Consider a very simple model of the New Zealand housing market in which there is a fixed supply of identical houses that will not change over time, and an unchanging demand. Let there be no on-going maintenance or other costs to owning a house, just the one-off capital costs. Finally, let there be a risk-free interest rate of 5%, let demanders be risk-neutral and indifferent between renting and owning for a given cost, and let rental income to a landlord be exempt from tax so that there is no tax advantage to owner-occupied housing. In this world, there would be an unchanging equilibrium rental price for housing over time, and an unchanging price of houses that would be equal to this rental price times 20.

Following on from Seamus’s later tweaks to the base model, let us also change the model a bit. Imagine that demand in one year’s time will double and then stay constant from then on, and that everyone knows that as of tomorrow. The process is identical to the one Seamus lays out for the case where only foreigners know that equilibrium demand doubles in a year’s time given that the stock of foreign capital is large relative to the domestic market:

In this version of the model, the rental rate would continue to remain constant for a year before doubling, but foreigners would bid up the price of houses now to the point where the capital gain between now and in one-year’s time was sufficient to exactly offset the fact that current rentals are insufficient to cover the capital cost of the house.

We can get a disconnect between current rental prices and current house prices where the market expects a future increase in demand relative to supply. That rental rates have not gone up lock-step with Auckland housing prices simply isn’t automatically evidence of a bubble or anything irrational. Rational, forward-looking investors could easily be looking at the current Auckland market, the current plans for expanding housing supply in Auckland, and concluding that there’s no way that supply will increase quickly enough to keep up with increases in demand. We can’t guarantee that this is what’s happening, but we cannot simply look at the purported disconnect between rental costs and property prices and conclude BUBBLE.

Now, consider the RBNZ’s proposed LVR policy. The policy restricts banks against allowing more than some percentage of new home mortgage loans to have “small” deposits. I am not sure if RBNZ has yet indicated what the thresholds for the different speed limits will be, but it’s sounded like it’s designed to be binding most of the time. Under what scenarios does this rule make sense?

Start with a world like Seamus’s: perfectly inelastic supply, prices 20 times rental rates under his conditions. Further, there is zero chance of bank bailouts in case of property market collapse; everything would be handled under OBR where depositors might take a small(ish) haircut. Individual investors form expectations about future demand; banks form estimates of the future price paths of housing. They’re both identical in this simple case. Now, suppose that a cohort of buyers knows that demand will double next year and so start bidding up the price of housing today. The banks from whom they’re borrowing money check to make sure that the buyers will be able to cover the mortgage costs and that the buyers’ expectations around future rental earnings aren’t crazy.

In this world, LVR restrictions only make sense where bank exposure to highly leveraged property loans impose systemic unpriced risk. Even if RBNZ knows no better than do individual banks, they might want to set speed limits where loans risk pushing into leverage levels consistent with prior cascading bank failures. I’d expect that RBNZ has run plenty of stress tests and has some idea of what level of leverage could yield cascading failures for varying levels of property leverage and plausible ranges of housing market drops.

But, in this world, you only set the speed limit to bind in exceptional cases, not in normal cases. To get a rule that binds more strictly, I think you have to assume that RBNZ knows more about the future path of relative demand (either shifts in demand, or potential moves in the supply curve) than do either the banks or investors.

I wonder whether Labour’s “dey turk er houses” ban-the-foreigners housing policy shares some common assumptions with RBNZ’s LVR regs. Tweak Seamus’s model a little bit such that these foreign investors are all just systematically wrong about the future demand path and that there are enough of them that they can manage to affect prices at the margin. Then banning them from bidding up housing where we know that they are causing a bubble by definition avoids a bubble. I do think this requires some pretty heroic assumptions about knowledge asymmetries. But they might not be all that far from the knowledge assumptions required to make sensible an LVR policy that binds in the normal rather than only in the exceptional case.

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